The injective model structure on \({{S}\mathrm {et}_{\hspace{-0.85355pt}\Delta }}\)  is cofibrantly generated (see e.g. [1]}), with generating cofibrations
\(\mathcal {I}= \big \lbrace  (\partial \Delta ^n \boxtimes \Delta ^0 \hookrightarrow \Delta ^n \boxtimes \Delta ^0)\square (\Delta ^0 \boxtimes \partial \Delta ^m \hookrightarrow \Delta ^0 \boxtimes \Delta ^m)\, \big | \, n,m \in \mathbb {N}_0 \big \rbrace \) 
